Suppose Eratosthenes had measured the length of a shadow at Syene and then compared it with the shadow measured not at Alexandria, but at a location half way between Syene and Alexandria-both measurements being made at the summer solstice. What would he have found?
A)The difference in the lengths of these shadows would have been greater than that found by comparing Syene and Alexandria, suggesting a larger value for the circumference of Earth than what he actually found.
B)The difference in the lengths of these shadows would have been larger than that found by comparing Syene and Alexandria, suggesting a smaller value for the circumference of Earth than what he actually found.
C)The difference in the lengths of these shadows would have been smaller than that found by comparing Syene and Alexandria.
D)The difference in the lengths of these shadows would have been the same as that found by comparing Syene with Alexandria.

Question

Quizplus · Accepted Answer

The difference in the lengths of these shadows would have been smaller because the location halfway between Syene and Alexandria would have a shadow length difference that is proportional to the smaller distance between this midpoint and Syene, compared to the original larger distance between Syene and Alexandria.

Suppose Eratosthenes Had Measured the Length of a Shadow at Syene